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Derivative of:
Derivative of 6^x
Derivative of (x+3)^4
Derivative of x^2+3x
Derivative of arctanx
Identical expressions
lg^ two (x- two)
lg squared (x minus 2)
lg to the power of two (x minus two)
lg2(x-2)
lg2x-2
lg²(x-2)
lg to the power of 2(x-2)
lg^2x-2
Similar expressions
lg^2(x+2)

The derivative of the function/ lg^2(x-2)

Derivative of lg^2(x-2)

The solution

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   2       
log (x - 2)

$$\log{\left(x - 2 \right)}^{2}$$

log(x - 2)^2

Detail solution

Let $u = \log{\left(x - 2 \right)}$ .
Apply the power rule: $u^{2}$ goes to $2 u$
Then, apply the chain rule. Multiply by $\frac{d}{d x} \log{\left(x - 2 \right)}$ :
1. Let $u = x - 2$ .
2. The derivative of $\log{\left(u \right)}$ is $\frac{1}{u}$ .
3. Then, apply the chain rule. Multiply by $\frac{d}{d x} \left(x - 2\right)$ :
  1. Differentiate $x - 2$ term by term:
    1. Apply the power rule: $x$ goes to $1$
    2. The derivative of the constant $-2$ is zero.
    The result is: $1$
  The result of the chain rule is:
  
  $\frac{1}{x - 2}$
The result of the chain rule is:

$\frac{2 \log{\left(x - 2 \right)}}{x - 2}$
Now simplify:

$\frac{2 \log{\left(x - 2 \right)}}{x - 2}$

The answer is:

$\frac{2 \log{\left(x - 2 \right)}}{x - 2}$

The graph

Plot the graph f(x)

Plot the graph f'(x)

The first derivative [src]

2*log(x - 2)
------------
   x - 2

$$\frac{2 \log{\left(x - 2 \right)}}{x - 2}$$

Simplify

The second derivative [src]

2*(1 - log(-2 + x))
-------------------
             2     
     (-2 + x)

$$\frac{2 \left(1 - \log{\left(x - 2 \right)}\right)}{\left(x - 2\right)^{2}}$$

Simplify

The third derivative [src]

2*(-3 + 2*log(-2 + x))
----------------------
              3       
      (-2 + x)

$$\frac{2 \left(2 \log{\left(x - 2 \right)} - 3\right)}{\left(x - 2\right)^{3}}$$

Simplify